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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="countr_zero.html" title="cpp/numeric/countr zero"><span class="t-lines"><span>countr_zero</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
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<tr class="t-nv-h1"><td colspan="5"> 成员函数</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/complex.html" title="cpp/numeric/complex/complex"><span class="t-lines"><span>complex::complex</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator%3D.html" title="cpp/numeric/complex/operator="><span class="t-lines"><span>complex::operator=</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/real.html" title="cpp/numeric/complex/real"><span class="t-lines"><span>complex::real</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/imag.html" title="cpp/numeric/complex/imag"><span class="t-lines"><span>complex::imag</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator_arith.html" title="cpp/numeric/complex/operator arith"><span class="t-lines"><span>complex::operator+=</span><span>complex::operator-=</span><span>complex::operator*=</span><span>complex::operator/=</span></span></a></div></div></td></tr>
<tr class="t-nv-h1"><td colspan="5"> 非成员函数</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator_arith2.html" title="cpp/numeric/complex/operator arith2"><span class="t-lines"><span>operator+</span><span>operator-</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator_arith3.html" title="cpp/numeric/complex/operator arith3"><span class="t-lines"><span>operator+</span><span>operator-</span><span>operator*</span><span>operator/</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator_cmp.html" title="cpp/numeric/complex/operator cmp"><span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div><div><span class="t-lines"><span></span><span><span class="t-mark-rev t-until-cxx20">(C++20 前)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator_ltltgtgt.html" title="cpp/numeric/complex/operator ltltgtgt"><span class="t-lines"><span>operator&lt;&lt;</span><span>operator&gt;&gt;</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/real2.html" title="cpp/numeric/complex/real2"><span class="t-lines"><span>real</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/imag2.html" title="cpp/numeric/complex/imag2"><span class="t-lines"><span>imag</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/abs.html" title="cpp/numeric/complex/abs"><span class="t-lines"><span>abs</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/arg.html" title="cpp/numeric/complex/arg"><span class="t-lines"><span>arg</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/norm.html" title="cpp/numeric/complex/norm"><span class="t-lines"><span>norm</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/conj.html" title="cpp/numeric/complex/conj"><span class="t-lines"><span>conj</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/proj.html" title="cpp/numeric/complex/proj"><span class="t-lines"><span>proj</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/polar.html" title="cpp/numeric/complex/polar"><span class="t-lines"><span>polar</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/operator%2522%2522i.html" title='cpp/numeric/complex/operator""i'><span class="t-lines"><span>operator""i</span><span>operator""if</span><span>operator""il</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx14">(C++14)</span></span><span><span class="t-mark-rev t-since-cxx14">(C++14)</span></span><span><span class="t-mark-rev t-since-cxx14">(C++14)</span></span></span></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 指数函数</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/exp.html" title="cpp/numeric/complex/exp"><span class="t-lines"><span>exp</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/log.html" title="cpp/numeric/complex/log"><span class="t-lines"><span>log</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/log10.html" title="cpp/numeric/complex/log10"><span class="t-lines"><span>log10</span></span></a></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 幂函数</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/pow.html" title="cpp/numeric/complex/pow"><span class="t-lines"><span>pow</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/sqrt.html" title="cpp/numeric/complex/sqrt"><span class="t-lines"><span>sqrt</span></span></a></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 三角函数</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/sin.html" title="cpp/numeric/complex/sin"><span class="t-lines"><span>sin</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cos.html" title="cpp/numeric/complex/cos"><span class="t-lines"><span>cos</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/tan.html" title="cpp/numeric/complex/tan"><span class="t-lines"><span>tan</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/asin.html" title="cpp/numeric/complex/asin"><span class="t-lines"><span>asin</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/acos.html" title="cpp/numeric/complex/acos"><span class="t-lines"><span>acos</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/atan.html" title="cpp/numeric/complex/atan"><span class="t-lines"><span>atan</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 双曲函数</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/sinh.html" title="cpp/numeric/complex/sinh"><span class="t-lines"><span>sinh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cosh.html" title="cpp/numeric/complex/cosh"><span class="t-lines"><span>cosh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/tanh.html" title="cpp/numeric/complex/tanh"><span class="t-lines"><span>tanh</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/asinh.html" title="cpp/numeric/complex/asinh"><span class="t-lines"><span>asinh</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/acosh.html" title="cpp/numeric/complex/acosh"><span class="t-lines"><span>acosh</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/atanh.html" title="cpp/numeric/complex/atanh"><span class="t-lines"><span>atanh</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
</table></div></td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div></div>
<table class="t-dcl-begin"><tbody>
<tr class="t-dsc-header">
<td> <div>定义于头文件 <code><a href="../header/complex.html" title="cpp/header/complex">&lt;complex&gt;</a></code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;</span> <span class="kw1">class</span> T <span class="sy1">&gt;</span><br>
<span class="kw1">class</span> complex<span class="sy4">;</span></span></div></td>
<td> (1) </td>
<td class="t-dcl-nopad">  </td>
</tr>
<tr class="t-dcl">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;&gt;</span> <span class="kw1">class</span> complex<span class="sy1">&lt;</span><span class="kw4">float</span><span class="sy1">&gt;</span><span class="sy4">;</span></span></div></td>
<td> (2) </td>
<td class="t-dcl-nopad">  </td>
</tr>
<tr class="t-dcl">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;&gt;</span> <span class="kw1">class</span> complex<span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span><span class="sy4">;</span></span></div></td>
<td> (3) </td>
<td class="t-dcl-nopad">  </td>
</tr>
<tr class="t-dcl">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;&gt;</span> <span class="kw1">class</span> complex<span class="sy1">&lt;</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">&gt;</span><span class="sy4">;</span></span></div></td>
<td> (4) </td>
<td class="t-dcl-nopad">  </td>
</tr>
<tr class="t-dcl-sep"><td></td><td></td><td></td></tr>
</tbody></table>
<p>模板特化 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">float</span><span class="sy1">&gt;</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span></span></span> 及 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">&gt;</span></span></span> 是表示并计算<a href="https://en.wikipedia.org/wiki/Complex_number" class="extiw" title="enwiki:Complex number">复数</a>的<a href="../named_req/LiteralType.html" title="cpp/named req/LiteralType"><i>字面类型</i> <span style="font-family: Georgia, 'DejaVu Serif', serif; font-style:italic">(LiteralType)</span> </a>。 
</p><p>对任何其他类型，实例化模板 <code>complex</code> 的效果是不确定的。
</p>
<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E7.B1.BB.E5.9E.8B">成员类型</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc-sep">
<td colspan="2">  
</td></tr>
<tr class="t-dsc-hitem">
<td>  成员类型
</td>
<td>  定义
</td></tr>


<tr class="t-dsc">
<td>  <code>value_type</code>
</td>
<td>  <code>T</code>
</td></tr>
</table>
<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">成员函数</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div t-dsc-member-nobold-div"><div><a href="complex/complex.html" title="cpp/numeric/complex/complex"> <span class="t-lines"><span>(构造函数)</span></span></a></div></div>
</td>
<td>  构造一个复数 <br> <span class="t-mark">(公开成员函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator%3D.html" title="cpp/numeric/complex/operator="> <span class="t-lines"><span>operator=</span></span></a></div></div>
</td>
<td>  赋值内容 <br> <span class="t-mark">(公开成员函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/real.html" title="cpp/numeric/complex/real"> <span class="t-lines"><span>real</span></span></a></div></div>
</td>
<td>  访问复数的实部 <br> <span class="t-mark">(公开成员函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/imag.html" title="cpp/numeric/complex/imag"> <span class="t-lines"><span>imag</span></span></a></div></div>
</td>
<td>   访问复数的虚部  <br> <span class="t-mark">(公开成员函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator_arith.html" title="cpp/numeric/complex/operator arith"> <span class="t-lines"><span>operator+=</span><span>operator-=</span><span>operator*=</span><span>operator/=</span></span></a></div></div>
</td>
<td>  两个复数，或一个复数与一个标量的复合赋值 <br> <span class="t-mark">(公开成员函数)</span> </td></tr>
</table>
<h3><span class="mw-headline" id=".E9.9D.9E.E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">非成员函数</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator_arith2.html" title="cpp/numeric/complex/operator arith2"> <span class="t-lines"><span>operator+</span><span>operator-</span></span></a></div></div>
</td>
<td>  对复数运用一元运算符 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator_arith3.html" title="cpp/numeric/complex/operator arith3"> <span class="t-lines"><span>operator+</span><span>operator-</span><span>operator*</span><span>operator/</span></span></a></div></div>
</td>
<td>  在两个复数，或一个复数与一个标量上进行复数算术运算 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator_cmp.html" title="cpp/numeric/complex/operator cmp"> <span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div><div><span class="t-lines"><span></span><span><span class="t-mark-rev t-until-cxx20">(C++20 中移除)</span></span></span></div></div>
</td>
<td>  比较两个复数，或一个复数与一个标量  <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator_ltltgtgt.html" title="cpp/numeric/complex/operator ltltgtgt"> <span class="t-lines"><span>operator&lt;&lt;</span><span>operator&gt;&gt;</span></span></a></div></div>
</td>
<td>  复数的序列化和反序列化 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/real2.html" title="cpp/numeric/complex/real2"> <span class="t-lines"><span>real</span></span></a></div></div>
</td>
<td>  返回实部 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/imag2.html" title="cpp/numeric/complex/imag2"> <span class="t-lines"><span>imag</span></span></a></div></div>
</td>
<td>  返回虚部 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/abs.html" title="cpp/numeric/complex/abs"> <span class="t-lines"><span>abs<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  返回复数的模 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/arg.html" title="cpp/numeric/complex/arg"> <span class="t-lines"><span>arg</span></span></a></div></div>
</td>
<td>  返回辐角 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/norm.html" title="cpp/numeric/complex/norm"> <span class="t-lines"><span>norm</span></span></a></div></div>
</td>
<td>  返回模(范数)的平方 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/conj.html" title="cpp/numeric/complex/conj"> <span class="t-lines"><span>conj</span></span></a></div></div>
</td>
<td>  返回复共轭 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/proj.html" title="cpp/numeric/complex/proj"> <span class="t-lines"><span>proj</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  返回到黎曼球上的投影 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/polar.html" title="cpp/numeric/complex/polar"> <span class="t-lines"><span>polar</span></span></a></div></div>
</td>
<td>  从模和辐角构造复数 <br> <span class="t-mark">(函数模板)</span> </td></tr>


<tr>
<td colspan="2"> <h5> <span class="mw-headline" id=".E6.8C.87.E6.95.B0.E5.87.BD.E6.95.B0">  指数函数 </span></h5>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/exp.html" title="cpp/numeric/complex/exp"> <span class="t-lines"><span>exp<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>   以 <i>e</i> 为底复数的指数  <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/log.html" title="cpp/numeric/complex/log"> <span class="t-lines"><span>log<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  沿负实轴切割的复自然对数 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/log10.html" title="cpp/numeric/complex/log10"> <span class="t-lines"><span>log10<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  沿负实轴分割的复常用对数 <br> <span class="t-mark">(函数模板)</span> </td></tr>


<tr>
<td colspan="2"> <h5> <span class="mw-headline" id=".E5.B9.82.E5.87.BD.E6.95.B0">  幂函数 </span></h5>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/pow.html" title="cpp/numeric/complex/pow"> <span class="t-lines"><span>pow<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  复数幂，一或两个参数可为复数 <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/sqrt.html" title="cpp/numeric/complex/sqrt"> <span class="t-lines"><span>sqrt<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  右半平面范围中的复平方根 <br> <span class="t-mark">(函数模板)</span> </td></tr>


<tr>
<td colspan="2"> <h5> <span class="mw-headline" id=".E4.B8.89.E8.A7.92.E5.87.BD.E6.95.B0">  三角函数 </span></h5>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/sin.html" title="cpp/numeric/complex/sin"> <span class="t-lines"><span>sin<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的正弦（ <span class="mjax" style="display:none">\({\small\sin{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">sin(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/cos.html" title="cpp/numeric/complex/cos"> <span class="t-lines"><span>cos<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的余弦（ <span class="mjax" style="display:none">\({\small\cos{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">cos(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/tan.html" title="cpp/numeric/complex/tan"> <span class="t-lines"><span>tan<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的正切（ <span class="mjax" style="display:none">\({\small\tan{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tan(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/asin.html" title="cpp/numeric/complex/asin"> <span class="t-lines"><span>asin<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反正弦（ <span class="mjax" style="display:none">\({\small\arcsin{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcsin(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/acos.html" title="cpp/numeric/complex/acos"> <span class="t-lines"><span>acos<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反余弦（ <span class="mjax" style="display:none">\({\small\arccos{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arccos(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/atan.html" title="cpp/numeric/complex/atan"> <span class="t-lines"><span>atan<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反正切（ <span class="mjax" style="display:none">\({\small\arctan{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arctan(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>


<tr>
<td colspan="2"> <h5> <span class="mw-headline" id=".E5.8F.8C.E6.9B.B2.E5.87.BD.E6.95.B0">  双曲函数 </span></h5>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/sinh.html" title="cpp/numeric/complex/sinh"> <span class="t-lines"><span>sinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的双曲正弦（ <span class="mjax" style="display:none">\({\small\sinh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">sinh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/cosh.html" title="cpp/numeric/complex/cosh"> <span class="t-lines"><span>cosh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的双曲余弦（ <span class="mjax" style="display:none">\({\small\cosh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">cosh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/tanh.html" title="cpp/numeric/complex/tanh"> <span class="t-lines"><span>tanh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td>  计算复数的双曲正切（ <span class="mjax" style="display:none">\({\small\tanh{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">tanh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/asinh.html" title="cpp/numeric/complex/asinh"> <span class="t-lines"><span>asinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反双曲正弦（ <span class="mjax" style="display:none">\({\small\operatorname{arsinh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arsinh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/acosh.html" title="cpp/numeric/complex/acosh"> <span class="t-lines"><span>acosh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反双曲余弦（ <span class="mjax" style="display:none">\({\small\operatorname{arcosh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcosh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/atanh.html" title="cpp/numeric/complex/atanh"> <span class="t-lines"><span>atanh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td>  计算复数的反双曲正切（ <span class="mjax" style="display:none">\({\small\operatorname{artanh}{z} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">artanh(z)</span> ） <br> <span class="t-mark">(函数模板)</span> </td></tr>
</table>
<h3><span class="mw-headline" id=".E9.80.9A.E8.BF.87.E6.95.B0.E7.BB.84.E8.AE.BF.E9.97.AE">通过数组访问</span></h3>
 <table class="t-rev-begin">
<tr class="t-rev t-since-cxx11"><td>
<p>对于任何 <code>complex&lt;T&gt;</code> 类型的对象 <code>z</code> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1">&lt;</span>T<span class="br0">(</span><span class="sy3">&amp;</span><span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span><span class="sy1">&gt;</span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">[</span><span class="nu0">0</span><span class="br0">]</span></span></span> 为 z 的实部且 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1">&lt;</span>T<span class="br0">(</span><span class="sy3">&amp;</span><span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span><span class="sy1">&gt;</span><span class="br0">(</span>z<span class="br0">)</span><span class="br0">[</span><span class="nu0">1</span><span class="br0">]</span></span></span> 为 z 的虚部。
</p><p>对于任何名为 <code>p</code> 指向 <code>complex&lt;T&gt;</code> 数组元素的指针，及任何合法下标 <span class="t-c"><span class="mw-geshi cpp source-cpp">i</span></span> ， <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1">&lt;</span>T<span class="sy2">*</span><span class="sy1">&gt;</span><span class="br0">(</span>p<span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="sy2">*</span>i<span class="br0">]</span></span></span> 等于复数 <span class="t-c"><span class="mw-geshi cpp source-cpp">p<span class="br0">[</span>i<span class="br0">]</span></span></span> 的实部，而 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw1">reinterpret_cast</span><span class="sy1">&lt;</span>T<span class="sy2">*</span><span class="sy1">&gt;</span><span class="br0">(</span>p<span class="br0">)</span><span class="br0">[</span><span class="nu0">2</span><span class="sy2">*</span>i <span class="sy2">+</span> <span class="nu0">1</span><span class="br0">]</span></span></span> 等于复数 <span class="t-c"><span class="mw-geshi cpp source-cpp">p<span class="br0">[</span>i<span class="br0">]</span></span></span> 的虚部 
</p><p>此要求的目的是 C++ 复数类型与 <a href="../../c/language/arithmetic_types.html#.E5.A4.8D.E6.B5.AE.E7.82.B9.E7.B1.BB.E5.9E.8B" title="c/language/arithmetic types">C 语言复数类型</a>（及其数组）的二进制兼容性，其中要求相同的对象表示。
</p>
</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td></tr>
</table>
<h3><span class="mw-headline" id=".E5.AE.9E.E7.8E.B0.E6.B3.A8.E8.A7.A3"> 实现注解 </span></h3>
 <table class="t-rev-begin">
<tr class="t-rev t-since-cxx11"><td>
<p>为满足数组访问的要求，实现需满足在单独且相邻的内存位置存储 <code>std::complex</code> 特化的实部和虚部。其非静态数据成员的可能声明包括：
</p>
<ul><li> 数组类型 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type<span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span></span></span> ，其首元素存有实部而第二元素存有虚部（例如 Microsoft Visual Studio ）；
</li><li> 单个 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type _Complex</span></span> 类型成员（封装对应的 <a href="../../c/language/arithmetic_types.html#.E5.A4.8D.E6.B5.AE.E7.82.B9.E7.B1.BB.E5.9E.8B" title="c/language/arithmetic types">C 语言复数类型</a>）（例如 GNU libstdc++ ）；
</li><li> 两个拥有相同访问权限的 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type</span></span> 类型成员，分别存有实部和虚部（例如 LLVM libc++ ）。
</li></ul>
<p>实现不能添加会占用与实部和虚部冲突的存储的非静态数据成员，而且必须确保类模板特化不含任何填充。实现也必须确保对数组访问的优化问题，其中要考虑到指向 <span class="t-c"><span class="mw-geshi cpp source-cpp">value_type</span></span> 的指针可能为 <code>std::complex</code> 特化的别名，对应的数组亦然。
</p>
</td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td></tr>
</table>
<h3><span class="mw-headline" id=".E5.AD.97.E9.9D.A2.E9.87.8F">字面量</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>定义于内联命名空间 <code>std::literals::complex_literals</code></div>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="complex/operator%2522%2522i.html" title='cpp/numeric/complex/operator""i'> <span class="t-lines"><span>operator""if</span><span>operator""i</span><span>operator""il</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx14">(C++14)</span></span></span></div></div>
</td>
<td>  表示纯虚数的 <span class="t-lc"><strong class="selflink">std::complex</strong></span> 字面量 <br> <span class="t-mark">(函数)</span> </td></tr>
</table>
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
<div class="t-example"><div class="t-example-live-link"><div class="coliru-btn coliru-btn-run-init">运行此代码</div></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="cpp source-cpp"><pre class="de1"><span class="co2">#include &lt;iostream&gt;</span>
<span class="co2">#include &lt;iomanip&gt;</span>
<span class="co2">#include &lt;complex&gt;</span>
<span class="co2">#include &lt;cmath&gt;</span>
 
<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
<span class="br0">{</span>
    <span class="kw1">using</span> <span class="kw1">namespace</span> std<span class="sy4">::</span><span class="me2">complex_literals</span><span class="sy4">;</span>
    <a href="../io/cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <a href="../io/manip/fixed.html"><span class="kw1783">std::<span class="me2">fixed</span></span></a> <span class="sy1">&lt;&lt;</span> <a href="../io/manip/setprecision.html"><span class="kw1795">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
 
    std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span> z1 <span class="sy1">=</span> 1i <span class="sy2">*</span> 1i<span class="sy4">;</span>     <span class="co1">// 虚数单位平方</span>
    <a href="../io/cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"i * i = "</span> <span class="sy1">&lt;&lt;</span> z1 <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
 
    std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span> z2 <span class="sy1">=</span> <a href="math/pow.html"><span class="kw1332">std::<span class="me2">pow</span></span></a><span class="br0">(</span>1i, <span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 虚数单位平方</span>
    <a href="../io/cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"pow(i, 2) = "</span> <span class="sy1">&lt;&lt;</span> z2 <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
 
    <span class="kw4">double</span> PI <span class="sy1">=</span> <a href="math/acos.html"><span class="kw1337">std::<span class="me2">acos</span></span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
    std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span> z3 <span class="sy1">=</span> <a href="math/exp.html"><span class="kw1321">std::<span class="me2">exp</span></span></a><span class="br0">(</span>1i <span class="sy2">*</span> PI<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 欧拉方程</span>
    <a href="../io/cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"exp(i * pi) = "</span> <span class="sy1">&lt;&lt;</span> z3 <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
 
    std<span class="sy4">::</span><span class="me2">complex</span><span class="sy1">&lt;</span><span class="kw4">double</span><span class="sy1">&gt;</span> z4 <span class="sy1">=</span> <span class="nu0">1</span>. <span class="sy2">+</span> 2i, z5 <span class="sy1">=</span> <span class="nu0">1</span>. <span class="sy2">-</span> 2i<span class="sy4">;</span> <span class="co1">// 共轭</span>
    <a href="../io/cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">"(1+2i)*(1-2i) = "</span> <span class="sy1">&lt;&lt;</span> z4 <span class="sy2">*</span> z5 <span class="sy1">&lt;&lt;</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div></div>
<p>输出：
</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="text source-text"><pre class="de1">i * i = (-1.0,0.0)
pow(i, 2) = (-1.0,0.0)
exp(i * pi) = (-1.0,0.0)
(1+2i)*(1-2i) = (5.0,0.0)</pre></div></div> 
</div>
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
<table class="t-dsc-begin">

</table>

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